Understanding Waves and Sound

Waves and Sound Overview

• Waves transfer energy without moving matter, acting as disturbances traveling through a medium in a periodic manner.
• The key learning objectives are describing hearing mechanisms, defining wave properties, and understanding ultrasound applications.

Types of Waves

• Waves are traveling disturbances that propagate energy from one location to another.
• Transverse waves exhibit oscillations perpendicular to the direction of wave travel.
• Longitudinal waves feature oscillations parallel to the direction of wave travel.
• Water waves display a combination of both transverse and longitudinal characteristics.

Periodic Waves

• Periodic waves are composed of repeating cycles or patterns generated continuously by a source.
• Each segment of a string within periodic waves oscillates in simple harmonic motion.
• Amplitude (A) represents the maximum displacement of a particle from its undisturbed position.
• Wavelength (λ) is the length of one complete wave cycle.
• Period (T) denotes the time needed for one full cycle to occur.
• Frequency (f) is the measure of how many cycles occur per unit of time, with the equation f=1/T
• Frequency is measured in Hertz (Hz) or inverse seconds (s⁻¹).

Sound Waves

• Sound waves are longitudinal, vibrating molecules within a medium like air.
• Pitch correlates with frequency of the sound wave.
• "Sound pitch" refers to the subjective perception of a sound wave's frequency.
• Loudness relies primarily on the pressure amplitude of the wave.

Speed of Sound

• Sound travels at varying speeds through different states of matter: gases, liquids, and solids.
• Sound travels at 331 m/s in air at 0 degrees Celsius, increasing to 343 m/s at 20 degrees Celsius
• Sound travels at 1004 m/s in Chloroform at 20 degrees Celsius
• The speed of sound in steel is 5960 m/s
• A rule of thumb estimates thunderstorm distance by counting seconds between lightning and thunder, and dividing by five to approximate miles.

Sound Intensity

• Sound waves carry energy and can perform work.
• Power is the energy transported per second.
• Sound intensity (I) quantifies power passing perpendicularly through a surface area, I=P/A, where P is power and A is area.

Decibels (dB)

• Decibels (dB) serve as a unit to compare sound intensities using a logarithmic scale.
• Logarithmic scale is used because of how the human hearing mechanism responds to intensity
• Intensity level (β in dB) is calculated as: β = (10 dB) log(I/I₀), where I₀ = 1.00 × 10⁻¹² W/m².
• Relative to the threshold of hearing (1.0 x 10^-12), rustling leaves measure 10 dB, a whisper 20 dB, normal conversation 65 dB, and a live rock concert 120 dB
• The threshold of pain is at 130 dB, while threshold of hearing is 0dB
• When the sound intensity equals the hearing threshold, the intensity level is zero because log(1) = 0.

Superposition and Interference

• Constructive interference occurs when two waves meet with condensation aligning with condensation, resulting in a reinforced wave.
• Destructive interference happens when condensation meets rarefaction, leading to wave cancellation.

Beats

• Beats arise from the superposition of two waves with slightly differing frequencies.
• The beat frequency equals the difference between the two original sound frequencies.

Physics of Hearing

• Hearing is the perception of sound, leveraging the ear's sensitivity to a substantial range of frequencies and intensities.
• The brain interprets simple information—pitch, loudness, direction—into complex thoughts and actions.
• Compressional waves travel through the ear canal (1-3).
• The eardrum (4) passes vibrations to three ossicles (5), amplifying the sound.
• Waves transform into nerve impulses via the cochlea (6).
• Auditory nerve bundles transmits nerve impulses to the brain (7).
• Healthy human ears perceive frequencies from 20 Hz to 20,000 Hz, with peak sensitivity between 2000 Hz and 5000 Hz at ~60 dB.
• Age-related damage to cochlear hairs can cause hearing loss.

Ultrasonic and Infrasonic Waves

• Ultrasonic waves exceed 20,000 Hz
• Dogs can perceive sounds up to approximately 50,000 Hz.
• Bats and dolphins use echolocation.
• Ultrasonic waves are used in medicine for diagnosis and therapy.
• Infrasonic waves are those below 20 Hz, also known as subsonic frequencies.
• Infrasonic waves cannot be heard
• You can feel infrasonic waves as rumble

Ultrasound

• Ultrasound uses sound waves above the human hearing range.
• Ultrasound devices operate between 20 kHz to several GHz for medical applications.
• Medical ultrasound ranges exceeding 2MHz
• Acoustic impedance (Z) is calculated by Z = ρ * v.
• ρ represents the medium's density.
• v is the sound velocity in the medium.
• The greater the difference in impedance, the more sound will be reflected, less transmitted
• The Unit of acoustic impedance is Pa.s/m³
• Air, water, blood, fat, muscle and bone all have varying densities.

Applications of Ultrasound

• Ultrasonic waves are focusable and adjustable in frequency and intensity.
• Ultrasound can detect objects, similar to echolocation, but has limited resolution based on wavelength and detail.
• Ultrasonic waves are used in both therapy and diagnosis
• Ultrasound therapy can shatter gallstones, pulverize tumors, and provide deep-heat therapy to injured muscles (diathermy).
• Cavitron Ultrasonic Surgical Aspirators (CUSA) uses ultrasonic sound
• CUSA destroys and removes brain tumors through a small probe oscillating at 23 kHz.
• CUSA probe pulverizes sections of the tumor with contact
• Debris is flushed with saline, which allows surgeons to specifically target malignant tissue.
• High-frequency sound pulses are emitted by a transducer.
• Wave energy is reflected back, its intensity is measured by a detector
• At tissue boundaries, some energy is reflected and some continues.
• Different tissues reflect and absorb energy differently.
• A 2-D cross-sectional image is obtained by scanning ultrasonic waves across the body detecting echoes at various locations.
• 3-D ultrasound combines numerous 2-D images from various angles.

Ultrasound Imaging

• A-scan ultrasound provides unidimensional depth information of tissue boundaries using pulse-echo methods.
• B-scan ultrasound utilizes narrow beams to create continuous, real-time images.
• M-scan ultrasound tracks moving targets, like heart valves, with a series of pulse echoes over time.

Doppler Effect

• The Doppler effect is a change in perceived frequency or pitch due to relative motion between a sound source and an observer.
• When a sound source is moving toward a stationary observer: fo= fs * (v/(v-vs)).
• v: Sound velocity
• vs: Moving source velocity
• fo: Observed frequency
• fs: Frequency produced by the moving source
• When a sound source is moving away from a stationary observer: fo= fs * (v/(v+vs)).

Doppler Ultrasound

• A transducer emits ultrasound to frequency f, and its reflected back through a moving blood.
• Changes in frequency will occur
• In 2-way motion
• In blood the angle of degree must be oblique
• The transducer emits ultrasound of frequency f, and gets reflected back by moving blood.